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arXiv · 1311.0125

Reductions of the Navier-Stokes-Allen-Cahn and the Navier-Stokes-Cahn-Hilliard equations

Heinrich Freistuhler·Matthias Kotschote
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Abstract

This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard equations, both of which consist of equations for the (total) fluid density rho, the (mass-averaged)velocity u and the concentration (of one of the phases,) c. Assuming in either case that both phases are incompressible with different densities, each of the models is shown to reduce to a system of evolution equations in rho and u alone. In the case of the Navier-Stokes-Allen-Cahn model, this reduced system is the classical Navier-Stokes-Korteweg model. The reduced system resulting from the Navier-Stokes-Cahn-Hilliard equations is a novel `integro'-differential system in which a non-local operator acts on the divergence of the velocity.

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Heinrich Freistuhler, Matthias Kotschote. 2013-11-01. Reductions of the Navier-Stokes-Allen-Cahn and the Navier-Stokes-Cahn-Hilliard equations. https://arxiv.org/abs/1311.0125

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